Green’s Dictionary of Slang

(UK tramp) a rag, ragged clothing.

1869		J.C. Parkinson Places and People 222: This figure was clothed in carpet. [...] It had a notice under it, that any person tearing up clothes in Billericay workhouse would be provided with a suit of the above description, [...] it had the desired effect, and the guardians were rarely troubled by a ‘tear-up.’.
1873		Appleton’s Journal (N.Y.) 6 Sept. 307/2: Even picked bones and the lousy ‘tear-ups’ (rags) cast behind the fences – are all made to do service in this literature of vagabonds.
1881		Dundee Courier (Scot.) 11 Feb. 7/5: A regular rig out of moleskin; that’s what it is. I done a tear-up here before.